Backdoor sets of quantified boolean formulas

Journal of Automated Reasoning

Volumn 42, Issue 1, 2009, Pages 77-97

  Samer, Marko ^a   Szeider, Stefan ^b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Backdoor sets; Parameterized complexity; Quantified Boolean formulas; Variable dependencies

Indexed keywords

PACKET NETWORKS; PROGRAMMING THEORY;

BACKDOOR SETS; BOOLEAN FORMULAE; BOUNDED TREEWIDTH; CNF FORMULAS; PARAMETERIZED COMPLEXITY; PROPOSITIONAL FORMULAS; QUANTIFIED BOOLEAN FORMULAS; SIDE PRODUCTS; TRACTABLE CLASS; VARIABLE DEPENDENCIES;

BOOLEAN FUNCTIONS;

EID: 59849129330     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-008-9114-5     Document Type: Article

References (39)

1. Abu-Khzam, F.N.: Kernelization algorithms for d-hitting set problems. In: Proc. 10th International Workshop on Algorithms and Data Structures (WADS'07), LNCS, vol. 4619, pp. 434-445. Springer, New York (2007)
2. B. Aspvall M.F. Plass R.E. Tarjan 1979 A linear-time algorithm for testing the truth of certain quantified Boolean formulas Inf. Process. Lett. 8 3 121 123
3. Ayari, A., Basin, D.: Qubos: Deciding quantified Boolean logic using propositional satisfiability solvers. In: Proc. 4th International Conference on Formal Methods in Computer-Aided Design (FMCAD'02), LNCS, vol. 2517, pp. 187-201. Springer, New York (2002)
4. Benedetti, M.: Quantifier trees for QBFs. In: Proc. 8th International Conference on Theory and Applications of Satisfiability Testing (SAT'05), LNCS, vol. 3569, pp. 378-385. Springer, New York (2005)
5. Biere, A.: Resolve and expand. In: Proc. 7th International Conference on Theory and Applications of Satisfiability Testing (SAT'04), LNCS, vol. 3542, pp. 59-70. Springer, New York (2005)
6. Bubeck, U., Kleine Büning, H.: Bounded universal expansion for preprocessing QBF. In: Proc. 10th International Conference on Theory and Applications of Satisfiability Testing (SAT'07), LNCS, vol. 4501 of, pages 244-257. Springer, New York (2007)
7. Chen, J., Kanj, I.A., Xia, G.: Improved parameterized upper bounds for vertex cover. In: Proc. 31st International Symposium on Mathematical Foundations of Computer Science (MFCS'06), LNCS, vol. 4162, pp. 238-249. Springer, New York (2006)
8. Y. Crama O. Ekin P.L. Hammer 1997 Variable and term removal from Boolean formulae Discrete Appl. Math. 75 3 217 230
9. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999)
10. Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving advanced reasoning tasks using quantified Boolean formulas. In: Proc. 17th AAAI Conference on Artificial Intelligence (AAAI'00), pp. 417-422. AAAI, Menlo Park (2000)
11. Egly, U., Tompits, H., Woltran, S.: On quantifier shifting for quantified Boolean formulas. In: Proc. SAT'02 Workshop on Theory and Applications of Quantified Boolean Formulas, pp. 48-61. Informal Proceedings (2002)
12. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, New York (2006)
13. Hoffmann, J., Gomes, C., Selman, B.: Structure and problem hardness: Goal asymmetry and DPLL proofs in SAT-based planning. In: Proc. 16th International Conference on Automated Planning and Scheduling (ICAPS'06), pp. 284-293. AAAI, Menlo Park (2006)
14. Interian, Y.: Backdoor sets for random 3-SAT. In: Proc. 6th International Conference on Theory and Applications of Satisfiability Testing (SAT'03), pp. 231-238. Informal Proceedings (2003)
15. Kilby, P., Slaney, J.K., Thiébaux, S., Walsh, T.: Backbones and backdoors in satisfiability. In: Proc. 20th AAAI Conference on Artificial Intelligence (AAAI'05), pp. 1368-1373. AAAI, Menlo Park (2005)
16. H. Kleine Büning M. Karpinski A. Flögel 1995 Resolution for quantified Boolean formulas Inf. Comput. 117 1 12 18
17. Kleine Büning, H., Lettman, T.: Propositional Logic: Deduction and Algorithms. Cambridge University Press, Cambridge (1999)
18. Knuth, D.E.: The Art of Computer Programming, vol. 3: Sorting and Searching, chapter 5.2.2 Sorting by Exchanging, pp. 106-110. Addison-Wesley, Reading (1973)
19. Lynce, I., Marques-Silva, J.P.: Hidden structure in unsatisfiable random 3-SAT: An empirical study. In: Proc. 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'04), pp. 246-251. IEEE Computer Society, Los Alamitos (2004)
20. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)
21. R. Niedermeier P. Rossmanith 2003 An efficient fixed-parameter algorithm for 3-hitting set J. Discret. Algorithms 1 1 89 102
22. Nishimura, N., Ragde, P., Szeider, S.: Detecting backdoor sets with respect to Horn and binary clauses. In: Proc. 7th International Conference on Theory and Applications of Satisfiability Testing (SAT'04), pp. 96-103. Informal Proceedings (2004)
23. N. Nishimura P. Ragde S. Szeider 2007 Solving #SAT using vertex covers Acta Inform. 44 7-8 509 523
24. Otwell, C., Remshagen, A., Truemper, K.: An effective QBF solver for planning problems. In: Proc. International Conference on Modeling, Simulation and Visualization Methods and International Conference on Algorithmic Mathematics and Computer Science (MSV/AMCS'04), pp. 311-316. CSREA, Las Vegas (2004)
25. Pan, G., Vardi, M.Y.: Fixed-parameter hierarchies inside PSpace. In: Proc. 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), pp. 27-36. IEEE Computer Society, Los Alamitos (2006)
26. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
27. J. Rintanen 1999 Constructing conditional plans by a theorem-prover J. Artif. Intell. Res. 10 323 352
28. Ruan, Y., Kautz, H.A., Horvitz, E.: The backdoor key: A path to understanding problem hardness. In: Proc. 19th AAAI Conference on Artificial Intelligence (AAAI'04), pp. 124-130. AAAI, Menlo Park (2004)
29. Sabharwal, A., Ansotegui, C., Gomes, C., Hart, J., Selman, B.: QBF modeling: Exploiting player symmetry for simplicity and efficiency. In: Proc. 9th International Conference on Theory and Applications of Satisfiability Testing (SAT'06), LNCS, vol. 4121, pp. 382-395. Springer, New York (2006)
30. Samer, M.: Variable dependencies of quantified CSPs. In: Proc. 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR'08), LNCS, vol. 5330, pp. 512-527. Springer, New York (2008)
31. Samer, M., Szeider, S.: Backdoor sets of quantified Boolean formulas. In: Proc. 10th International Conference on Theory and Applications of Satisfiability Testing (SAT'07), LNCS, vol. 4501, pp. 230-243. Springer, New York (2007)
32. Samulowitz, H., Bacchus, F.: Binary clause reasoning in QBF. In: Proc. 9th International Conference on Theory and Applications of Satisfiability Testing (SAT'06), LNCS, vol. 4121, pp. 353-367. Springer, New York (2006)
33. Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Proc. 5th Annual ACM Symposium on Theory of Computing (STOC'73), pp. 1-9. ACM, New York (1973)
34. S. Szeider 2005 Backdoor sets for DLL subsolvers J. Autom. Reason. 35 1-3 73 88
35. S. Szeider 2005 Generalizations of matched CNF formulas Ann. Math. Artif. Intell. 43 1-4 223 238
36. Szeider, S.: Matched formulas and backdoor sets. In: Proc. 10th International Conference on Theory and Applications of Satisfiability Testing (SAT'07), LNCS, vol. 4501, pp. 94-99. Springer, New York (2007)
37. R.E. Tarjan 1972 Depth first search and linear graph algorithms SIAM J. Comput. 1 2 146 160
38. Williams, R., Gomes, C., Selman, B.: Backdoors to typical case complexity. In: Proc. 18th International Joint Conference on Artificial Intelligence (IJCAI'03), pp. 1173-1178. Morgan Kaufmann, San Francisco (2003)
39. Williams, R., Gomes, C., Selman, B.: On the connections between backdoors, restarts, and heavy-tailedness in combinatorial search. In: Proc. 6th International Conference on Theory and Applications of Satisfiability Testing (SAT'03), pp. 222-230. Informal Proceedings (2003)